On an energy conserving treatment of variable interfaces in a finite difference PE code

摘要

We consider the 'standard' and 'third-order' parabolic equations of underwater acoustics in a range-dependent medium consisting of two fluid layers with a variable interface and a horizontal bottom with an impedance boundary condition. For the discretization we use a second-order, implicit finite difference scheme coupled with a discrete analog of the impedance condition. At the interface, for the standard parabolic equation, we use discrete analogs of the approximate interface conditions imposed on a piecewise linear approximation to the interface curve by Lee and McDaniel [J. Acoust. Sec. Am. 73 (1983), 1441-1447]. We use the same discrete conditions in a related 'hybrid' scheme for the 'third-order' parabolic equation. We implement the resulting numerical scheme in a code, which we apply to two benchmark underwater acoustic problems with variable interfaces. The results are compared to those obtained by existing numerical codes in the literature. [References: 19]